The airline will use its 168-seater Boeing 737-800 aircraft on all these routes.
Singh, who has helmed the turnaround of the once ailing low cost carrier, said big bold reforms and more out of the box thinking can be expected from the government.
HSBC increased its price target for SpiceJet to Rs 115 from Rs 79.50 earlier.
SpiceJet will also introduce new daily flights on the Bengaluru-Belagavi-Bengaluru route.
The airline has taken at least 22 planes that were earlier used by Jet Airways, which temporarily shuttered its operations due to cash crunch in April.
In March, SpiceJet became the first Indian low cost carrier to take membership of the IATA, a grouping of around 290 airlines.
The airline company reported a net loss of Rs 316.1 crore in FY19 due to a Rs 427.5 crore loss in the first two quarters.
SpiceJet is the fourth domestic airline to achieve the feat after national carrier Air India, now defunct Jet Airways and rival IndiGo.
The new services, which include flights to regional destinations such as Thiruvananthapuram, Vijayawada and Tirupati from Mumbai, will be launched between May 26 and May 30.
The airline added that tickets are available at a special fare of Rs 12,399 (all-inclusive) for Mumbai–Jeddah trip and Rs 15,399 (all inclusive) for Jeddah-Mumbai trip.
Growth in the number of travellers is also expected to even out to 8-12 percent, due to the steep flight tickets.
IndiGo and GoAir offered heavy percent discounts on the price of tickets, while SpiceJet has added multiple routes to cater to the heavy summer travel numbers.
Jet Airway's temporary suspension leaves over 766 slots vacant at domestic airports in the country. The Slot Allocation Committee has allocated nearly 480 of Jet's slots to other airlines.
A SpiceJet spokesperson confirmed the return of its Chennai flight to Mumbai due to a "technical" issue.
The move comes after the airline leased some of the Boeing 737s from the grounded Jet Airways and entered into a code-share pact with Gulf carrier Emirates which is a full- service operator.
Jet's entire Boeing fleet, including the narrow-body B737s, had two class configurations--business and economy.
This the fourth time SpiceJet has been expanding its network in less than a month, particularly since the grounding of Jet Airways last month.
All the passengers and the crew, however, are safe, and efforts are on to tow away the aircraft from the runway and resume operations at the earliest, he said.
Singh said SpiceJet was planning to induct 40 aircraft of Jet Airways and was hiring a significant number of professionals from the troubled airline.
The two rivals from NCR have nearly matched each other's pace in adding flights. But, one has been more aggressive in adding aircraft.
SpiceJet said on April 23 the new flights from Mumbai are on the Mumbai-Jaipur-Mumbai, Mumbai-Amritsar-Mumbai, Mumbai-Mangalore-Mumbai and Mumbai-Coimbatore-Mumbai sectors.
Cash-strapped Jet Airways (including Jet lite), which decided to stop all its operations last week, saw a 65 percent YoY decline in pax traffic to 0.7 million in March.